A question paper has two parts, A and B, each containing 5 questions. If a student has to choose 3 from part A and 2 from part B, in how many ways can he choose the questions?

Question: A question paper has two parts, A and B, each containing 5 questions. If a student has to choose 3 from part A and 2 from part B, in how many ways can he choose the questions?

Solution:
ways to choose 3 from part A = ⁵C₃
ways to choose 2 from part B = ⁵C₂

choose 3 from part A and 2 from part B = ⁵C₃ × ⁵C₂
= {5!/(3! 2!)} × {5!/(2! 3!)}
= 10 × 10
= 100